Definition 1.4 ([1]}) 
Let \((X,{{F}},\Delta )\)  be a foliated triple and \(f : Y\rightarrow X\)  be a proper birational morphism.
For any divisor \(E\)  on \(Y\) , we define the discrepancy of \(({{F}},\Delta )\)  along \(E\)  to be \(a(E,{{F}},\Delta ) = \textnormal {ord}_E(K_{f^*{{F}}}-f^*(K_{{F}}+\Delta ))\) .
We say
\((X,{{F}},\Delta ) \mbox{ is } \left\lbrace \begin{array}{ll}\textnormal {terminal} & \mbox{ if } a(E,{{F}},\Delta )> 0 \\\textnormal {canonical} & \mbox{ if } a(E,{{F}},\Delta )\ge 0 \\\textnormal {log terminal} & \mbox{ if } a(E,{{F}},\Delta )> -\varepsilon (E) \\\textnormal {log canonical} & \mbox{ if } a(E,{{F}},\Delta )\ge -\varepsilon (E)\end{array}\right.\mbox{ for every divisor $E$ over $X$} \) 
